Since its invention by C. W. Musser (Patent Document 1), the strain wave gearing has been contrived in a variety of inventions and designs by many researchers including the present inventor(s), as well as Musser himself. There are even a variety of inventions related merely to the tooth profile of strain wave gearings. In Patent Document 2, the present inventor proposed using the basic tooth profile of the strain wave gearing as an involute tooth profile, and in Patent Documents 3 and 4 proposed using a technique in which a rack is used to approximate the meshing of the teeth of a rigid internally toothed gear and a flexible externally toothed gear in a strain wave gearing as a tooth-profile-designing method for deriving a tooth profile for the tooth ends of both gears, which have a large area of contact. In Patent Document 5, the present inventor proposed a high-ratchet-torque tooth profile enabling continuous meshing in a strain wave gearing.
Typically, strain wave gearings have a circular rigid internally toothed gear, a flexible externally toothed gear disposed coaxially within the internally toothed gear, and a wave generator fitted within the externally toothed gear. The flexible externally toothed gear comprises a flexible cylindrical barrel part, a diaphragm extending radially from a trailing end of the cylindrical barrel part, and external teeth formed on the outer peripheral portion of the leading end opening side of the cylindrical barrel part. A flexible externally toothed gear formed in a state where the diaphragm closes off the trailing end opening of the cylindrical barrel part is known as a cup-shaped flexible externally toothed gear, and a flexible externally toothed gear formed in a state where the diaphragm expands outward from the trailing end of the cylindrical barrel part is known as a top-hat-shaped flexible externally toothed gear. Flexible externally toothed gears of either shape are flexed into an ellipsoidal shape by the wave generator, and the external teeth formed on the outer peripheral portion of the cylindrical barrel part of either flexible externally toothed gear mesh with the internal teeth of the rigid internally toothed gear on both ends of the ellipsoid in the direction of the major axis.
When the flexible externally toothed gear is ellipsoidally deformed by the wave generator, the rim-neutral circle of the external teeth of the flexible externally toothed gear is also deformed into an ellipsoidal rim-neutral curve. Here, “rim-neutral circle” refers to a circle described by the line of intersection between a neutral surface and a transverse cross-section of the flexible externally toothed gear, where “neutral surface” refers to a surface passing through the thickness (root rim thickness) center of the root part of the flexible externally toothed gear while the flexible externally toothed gear is in a perfectly circular state before being flexed into an ellipsoidal shape, and “rim-neutral curve” refers to a curve after the rim-neutral circle has been flexed into an ellipsoidal shape. The ratio w/w0 is known as the “deflection coefficient κ,” where w is the degree of radial flexing relative to the pre-deformation rim-neutral circle at a major-axis position on the ellipsoidal rim-neutral curve, and the normal (standard) degree of flexing w0 is the value obtained by dividing the radius of the rim-neutral circle by the reduction ratio of the strain wave gearing. “Non-deflected flexing” refers to a case where the normal degree of flexing is obtained, “positive deflection flexing” refers to a case where a degree of flexing larger than the normal degree of flexing (κ>1) is obtained, and “negative deflection flexing” refers to a case where a degree of flexing smaller than the normal degree of flexing (κ<1) is obtained.
The degree of flexing along the tooth trace direction of the external teeth of the ellipsoidally flexed flexible externally toothed gear, from the trailing end part of the side of the diaphragm toward the leading end part of the leading end opening side, increases substantially in proportion with respect to the distance from the diaphragm. Individual portions of the external teeth of the flexible externally toothed gear undergo repeated radial flexing as the wave generator rotates. This flexing of the flexible externally toothed gear is known as “coning.” When the degree of flexing in a transverse cross-section in the tooth-trace-direction center of the external teeth is set as the normal degree of flexing (κ=1), a positive-deflection state of flexing will be assumed on the side of the external teeth closer to the leading end part, and a negative-deflection state of flexing will be assumed on the side closer to the trailing end part. An external-tooth profile in a state of positive deflection flexing across the entirety of the external teeth in the tooth trace direction is known as a “positive deflection tooth profile,” and an external-tooth profile in a state of negative deflection flexing across the entirety of the external teeth in the tooth trace direction is known as a “negative deflection tooth profile.”    [Patent Document 1] U.S. Pat. No. 2,906,134    [Patent Document 2] JP-B 45-41171    [Patent Document 3] JP-A 63-115943    [Patent Document 4] JP-A 64-79448    [Patent Document 5] JP-A 2007-211907